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1999 | 79 | 1 | 37-61
Tytuł artykułu

Charge transfer scatteringin a constant electric field

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We prove the asymptotic completeness of the quantum scattering for a Stark Hamiltonian with a time dependent interaction potential, created by N classical particles moving in a constant electric field.
Słowa kluczowe
Rocznik
Tom
79
Numer
1
Strony
37-61
Opis fizyczny
Daty
wydano
1999
otrzymano
1997-03-17
poprawiono
1998-05-12
Twórcy
  • Institut de Mathématiques de Paris-Jussieu, UMR 9994, Université Paris 7 (D. Diderot), 2 Place Jussieu, 75252 Paris Cedex 05, France
Bibliografia
  • [1] T. Adachi and H. Tamura, Asymptotic completeness for long range many-particle systems with Stark effect, J. Math. Sci. Univ. Tokyo 2 (1995), 77-116.
  • [2] T. Adachi and H. Tamura, Asymptotic completeness for long range many-particle systems with Stark effect. II, Comm. Math. Phys. 174 (1996), 537-559.
  • [3] W. O. Amrein, A. Boutet de Monvel and V. Georgescu, $L^p$-inequalities for the Laplacian and unique continuation, Ann. Inst. Fourier (Grenoble) 31 (1981), no. 3, 153-168.
  • [4] W. O. Amrein, A. Boutet de Monvel and V. Georgescu, $C_0$-Groups, Commutator Methods and Spectral Theory of N-Body Hamiltonians, Birkhäuser, 1996.
  • [5] J. E. Avron and I. W. Herbst, Spectral and scattering theory for Schrödinger operators related to Stark effect, Comm. Math. Phys. 52 (1977), 239-254.
  • [6] J. Dereziński and C. Gérard, Asymptotic Completeness of N-Particle Systems, Springer, 1996.
  • [7] G. M. Graf, Phase space analysis of the charge transfer model, Helv. Phys. Acta 63 (1990), 107-138.
  • [8] G. M. Graf, Asymptotic completeness for N-body short-range quantum systems: a new proof, Comm. Math. Phys. 123 (1990), 107-138.
  • [9] G. M. Graf, A remark on long-range Stark scattering, Helv. Phys. Acta 64 (1991), 1167-1174.
  • [10] G. A. Hagedorn, Asymptotic completeness for the impact parameter approximation to the three particle scattering, Ann. Inst. H. Poincaré, Sect. A 36 (1982), 19-40.
  • [11] B. Helffer et J. Sjöstrand, Equation de Schrödinger avec champ magnétique et équation de Harper, in: Lecture Notes in Phys. 345, Springer, 1989, 118-197.
  • [12] I. W. Herbst, Unitary equivalence of Stark effect Hamiltonians, Math. Z. 155 (1977), 55-70.
  • [13] I. W. Herbst, J. S. Mοller and E. Skibsted, Spectral analysis of N-body Stark Hamiltonians, Comm. Math. Phys. 174 (1995), 261-294.
  • [14] I. W. Herbst, J. S. Mοller and E. Skibsted, Asymptotic completeness for N-body Stark Hamiltonians, ibid. 174 (1996), 509-535.
  • [15] A. Jensen, Scattering theory for Stark Hamiltonians, Proc. Indian Acad. Sci. (Math. Sci.) 104 (1994), 599-651.
  • [16] A. Jensen and T. Ozawa, Existence and non-existence results for wave operators for perturbations of the Laplacian, Rev. Math. Phys. 5 (1993), 601-629.
  • [17] A. Jensen and K. Yajima, On the long range scattering for Stark Hamiltonians, J. Reine Angew. Math. 420 (1991), 179-193.
  • [18] E. L. Korotyaev, On the scattering theory of several particles in an external electric field, Math. USSR-Sb. 60 (1988), 177-196.
  • [19] P. A. Perry, Scattering Theory by the Enss Method, Math. Rep. 1, Harwood, 1983, 1-347.
  • [20] I. M. Sigal, Stark effect in multielectron systems: non-existence of bound states, Comm. Math. Phys. 122 (1989), 1-22.
  • [21] I. M. Sigal and A. Soffer, The N-particle scattering problem: asymptotic completeness for the short-range quantum systems, Ann. of Math. 125 (1987), 35-108.
  • [22] H. Tamura, Scattering theory for N-particle systems with Stark effect: asymptotic completeness, RIMS Kyoto Univ. 29 (1993), 869-884.
  • [23] D. A. White, The Stark effect and long-range scattering in two Hilbert spaces, Indiana Univ. Math. J. 39 (1990), 517-546.
  • [24] D. A. White, Modified wave operators and Stark Hamiltonians, Duke Math. J. 68 (1992), 83-100.
  • [25] U. Wüller, Geometric methods in scattering theory of the charge transfer model, ibid. 62 (1991), 273-313.
  • [26] K. Yajima, A multi-channel scattering theory for some time dependent hamiltonians, Charge Transfer Problem, Comm. Math. Phys. 75 (1980), 153-178.
  • [27] K. Yajima, Spectral and scattering theory for Schrödinger operators with Stark effect, J. Fac. Sci. Univ. Tokyo Sect. IA 26 (1979), 377-390.
  • [28] K. Yajima, Spectral and scattering theory for Schrödinger operators with Stark effect, II, ibid. 28 (1981), 1-15.
  • [29] L. Zieliński, Complétude asymptotique pour un modèle du transfert de charge, Ann. Inst. H. Poincaré Phys. Théor. 58 (1993), 363-411.
  • [30] L. Zieliński, Scattering for a dispersive charge transfer model, ibid. 65 (1997), 339-386.
  • [31] L. Zieliński, Asymptotic completeness for multiparticle dispersive charge transfer model, J. Funct. Anal. 150 (1997), 453-470.
  • [32] L. Zieliński, Dispersive charge transfer model with long range interactions, J. Math. Anal. Appl. 217 (1998), 43-71.
  • [33] J. Zorbas, Scattering theory for Stark Hamiltonians involving long range potentials, J. Math. Phys. 19 (1978), 577-580.
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Bibliografia
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